Short biography

Bruce Hardie is a Professor of Marketing at London Business School, UK. He holds a B.Com degree in Management Studies and an M.Com degree in Marketing at the University of Auckland, New Zealand, an M.A. in Managerial Science and Applied Economics, and a Ph.D. in Marketing at the University of Pennsylvania USA.

Hardie’s research focuses on developing data-based models that are easy to implement and use by marketing analysts and decision-makers. His current focus is on the development of probability models used in customer analysis. Hardie’s research appeared in numerous marketing, statistics, and operation research journals.

Bruce Hardie’s contribution to the Customer Value Optimization world

Customer-Base Analysis in a Discrete-Time Noncontractual Setting

By Peter S. Fader, Bruce G. S. Hardie, Jen Shang

In this paper, Hardie and his co-author present a beta-geometric/beta-Bernoulli (BG/BB) model that can help to predict the future customer behavior for companies that do not have a subscription-based business model.

The authors said that “the model is easy to implement in a standard spreadsheet environment and yields relatively simple closed-form expressions for the expected number of future transactions conditional on past observed behavior (and other quantities of managerial interest).

RFM’ and ‘CLV’: Using Iso-value Curves for Customer Base Analysis 

By Peter Fader, Bruce Hardie, Ka Lok Lee 

In this paper, the authors present a new model that links the RFM model and the customer lifetime value. Hardie and the co-authors suggest a formal model whose key to analysis is the “iso value” curve.

The authors explain why they have chosen this approach: 

Key to this analysis is the notion of ‘iso-value’ curves, which enable us to group together individual customers who have different behavioral histories but similar future valuations. Iso-value curves make it easy to visualize and summarize the main interactions and tradeoffs among the RFM measures and CLV.

“Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model

By Peter S. Fader, Bruce G. S. Hardie, Ka Lok Lee

In this paper, the authors suggest an alternative to predicting future customer purchasing patterns. Their new model is beta-geometric/NBD (BG/NBD) and is an alternative to the Pareto/NBD “Counting Your Customers” framework proposed by Schmittlein, Morrison, and Colombo.

The authors say that the parameters of their model can be obtained in Microsoft Excel:

We develop a new model, the beta-geometric/NBD (BG/NBD), which represents a slight

variation in the behavioral “story” associated with the Pareto/NBD, but it is vastly easier to


Can We Infer “Trial and Repeat” Numbers From Aggregate Sales Data? 

By Peter S. Fader, Bruce G. S. Hardie

In this paper, Hardie and Fader show that product performance monitoring and forecasting should be performed with caution when analyzing the trial and repeat purchase components. 

The authors explain their methodology:

“Using panel data for twenty new products, we aggregate the household-level transaction data to arrive at aggregate sales data. We fit a model of new product sales to these data and compare the implied trial/repeat patterns to the actual patterns observed using the raw panel data.”

They conclude that “any inferences derived from the aggregate sales data using such models can be very misleading.”

Modeling the Evolution of Repeat Buying 

By Peter S. Fader, Bruce G. S. Hardie

In this paper, the authors suggest a nonstationary model that can properly capture and forecast repeat buying behaviors.

What the authors suggest is an alternative to the negative binomial (NBD) model: 

We introduce a model — the nonstationary exponential-gamma (NSEG) model — that accomplishes these tasks while retaining the well-known robustness, interpretability, and other desirable properties of the basic NBD framework. […] We demonstrate that NSEG performs very well on both dimensions, especially in contrast to the benchmark NBD model.